The Fullest Thing You Own

In a workshop in Florence, sometime around the year 1660, a group of careful men set out to squeeze water until it gave up.

They had a hollow ball of gold, or so the story that reached John Locke went, and they filled it with water and closed it tight. Then they put it in a press driven by screws and turned the screws with all the force they could find. Their idea was simple. Water is soft. A little push moves it. A big enough push, they thought, should crush its tiny parts closer together and shrink it into a smaller space.

The screws bit down. The gold groaned. And then something happened that nobody had bet on. The water did not shrink. Instead it came through the wall of the ball. It pushed its way through the pores of the solid gold, out to the surface, where it stood up in fine beads like dew on cold glass and then rolled off in drops. The metal never had to give. The water would rather pass through gold than let its own parts crowd one hair closer together.

Sit with how strange that is. Gold is the heavy one, the dense one, the one you’d call solid without thinking. Water is the one that splashes and pours and takes any shape you like. Yet under the press it was the gold that turned out to be full of doors, and the soft, sloshing water that would not budge. Whatever “solid” means, it did not line up the way the men expected.

Hold on to that little scene. We are going to come back to it, and by the time we do, it is going to mean something completely different than it does right now.

The one thing you’re sure of

Let me start with the thing you already believe, because you believe it harder than almost anything else you know.

Two things cannot be in the same place at the same time.

Say it out loud and it sounds too obvious to bother saying. Of course they can’t. Your coffee cup is on the table, and the table is not also where the cup is; the cup pushed nothing aside because the tabletop is a surface, not a spot the cup could sink into. If you shove your two hands together, they stop. If you throw a ball at a wall, the ball comes back. Kick a stone and your foot learns its lesson. All day long, in a thousand tiny ways, the world tells you the same thing: stuff is stuff, stuff takes up room, and where there is already stuff, no more will fit.

This is what people call solidity, and it feels less like an opinion than like the floor under every other opinion. A cup that is full cannot hold more water. Not because of some rule you could argue with, but because there is already something there, and the something is in the way. Matter fills the space it sits in, the way water fills a glass to the brim, and once a space is filled, that’s that. You cannot walk through a closed door. You have never walked through a closed door. Nobody you know has ever walked through a closed door.

It’s such solid ground that it feels like there is nothing underneath it to explain. It doesn’t seem like a fact you learned. It seems like a fact the universe simply is. If someone asked you why two things can’t share a place, you might blink and say, well, because they’re both there. Because they’re solid. Because that’s what solid means.

Good. Keep that answer close. That answer is the thing this whole essay is about to take apart — not because it’s stupid, but because it’s the most reasonable answer in the world, and it’s still not right.

First, don’t ask

The first thinker we’ll bring in agrees with you so completely that he thinks the question isn’t even worth asking.

John Locke, writing in the 1600s, wanted to build all of human knowledge up from the simplest pieces the senses hand us. And when he looked for the simplest, most basic thing we learn from touch, he landed exactly where you did. He called it solidity: the fact that a body keeps every other body out of the space it holds, and that no force, however great, can make it share.

Locke thought this was the deepest idea we have about matter. Not color, not weight, not warmth — those come and go. But solidity, he said, is the one idea “most intimately connected with, and essential to body.” It is the thing that makes a body a body at all.

And here’s his move, the one worth marking. When you ask Locke what solidity actually is — what’s really going on when two things won’t share a place — he refuses to answer. “If any one ask me what this solidity is,” he writes, “I send him to his senses to inform him.” Put a stone, or a blown-up ball, between your two hands, he says, and try to bring your hands together, “and he will know.” That’s the whole explanation. There isn’t a deeper one. Solidity is a brute fact you feel in your palms, and asking for the cause behind it is like asking someone to explain color to a blind man with words. You can’t get under it. You just meet it.

Notice what this does to your belief. It doesn’t challenge it. It cements it. The smartest careful thinker of his age looked at “two things can’t share a place,” decided it was bedrock, and told everyone to stop digging. Solid means solid. Send him to his senses. If you walked in confident, you should feel more confident now, not less.

Which is exactly the problem.

It feels like math, but it isn’t

Because there’s a second way people have tried to make sense of the rule, and it’s even stronger than Locke’s. It says: two things can’t share a place not just because they’re solid, but because sharing a place is impossible — impossible the way a square circle is impossible, impossible the way a triangle with four corners is impossible. Not a fact about the world. A fact about logic.

You can feel the pull of this. Picture a spot in space with exact edges — a little box. Now imagine two marbles both filling that box, both taking up every inch of it. But if marble A fills the whole box, and marble B fills the whole box, then A and B have the exact same size, the exact same shape, the exact same edges… so in what sense are they two? They look like one thing wearing two names. The great thinkers who took this line, going back to Aristotle, said that if you could pack two bodies into one place, you could pack in a thousand, and the smallest thimble could swallow the sea, “for many a little makes a mickle.” Once you let one extra thing in, there’s no honest place to stop. So you must let none in. Case closed, and closed by pure reason, not by any experiment.

If that argument holds, then “two things can’t share a place” isn’t a discovery about matter at all. It’s a truth of geometry, sitting in the same locked vault as the fact that a triangle’s angles add to a straight line. No press, no gold ball, no future science could ever touch it.

And then a medieval monk quietly pried the vault open.

Thomas Aquinas, in the 1200s, worked through this exact question — can two bodies be in one place? — with more care than almost anyone before him. He agreed that in the normal run of things, no, they can’t; the reason two bodies sit in two places is that they’re two lumps of matter, and separate lumps need separate spots. So far, standard.

But then he asked a sharper question. Is it impossible? Impossible like a square circle? Or just impossible for matter, the way matter happens to work? And his answer was that it is only the second kind. He argued, step by step, that two bodies in one place breaks no law of geometry and hides no contradiction — that a mind can hold the idea without the idea falling apart in its hands. It would take a miracle to actually do it, he said, reaching for the story of the risen Christ passing into a room “the doors being shut.” But — and this is the whole point — a miracle can only do a thing that is possible in the first place. No miracle can make a square circle, because a square circle is nonsense, and even divine power can’t make nonsense true. Aquinas is saying, plainly, that two bodies in one place is not nonsense. It’s just not how our world runs.

Feel the floor shift, even a little. A moment ago “two things can’t share a place” was locked in the vault with the truths of math, untouchable forever. Now a careful thinker has shown it was never in that vault. It’s not a truth of reason. It’s a fact about the particular stuff our world is made of — and facts about stuff are exactly the kind of thing that later discoveries are allowed to rewrite.

The question you thought had no cause — why can’t two things share a place — just became a live question again. And once it’s live, someone is going to go looking for the cause.

The scientist’s question

The someone was Isaac Newton, and to see what he did you have to notice that he asked a different kind of question than everyone before him.

Locke asked what solidity is and gave up. Aristotle and Aquinas asked whether the rule was necessary. Newton asked something that sounds almost boring next to those, and turned out to be the crack that split the whole thing open. He asked: where do we actually get this idea, and how sure are we allowed to be?

In the rules he laid down for doing physics, Newton listed the properties he was willing to treat as belonging to every body in the universe — things like being spread out in space, and being movable, and being impenetrable, his word for our rule about sharing a place. And when he came to impenetrability, he wrote one sentence that should have caused more of an earthquake than it did:

“That all bodies are impenetrable, we gather not from reason, but from sensation.”

Read that slowly. Not from reason. Newton, the most careful reasoner of his century, is telling you that the fact you were most sure of — the one that felt like the floor under everything — was never proved by thinking at all. We believe every body is impenetrable for one reason and one reason only: the bodies we’ve bumped into have been. We handled some things, they wouldn’t share space with our hands, and we spread that out over all matter everywhere, forever. It’s a habit built from touch. A very good habit. But a habit, not a law handed down from logic.

This is the ordinary, almost invisible move that changes everything, so let me say plainly what it costs you. If impenetrability is not a truth of reason, and it’s not a law of geometry, and it’s “gathered from sensation” — from a finite pile of things we happen to have squeezed — then it is exactly the sort of claim that has a cause underneath it. Locke told you to stop asking what solidity is. Newton, without quite meaning to, told you why that was the wrong order. Don’t ask what it is. Ask what makes it happen. Because if it’s a fact about the world rather than a fact about logic, then there’s machinery under it, and machinery can be opened up.

So open it up. When two things won’t share a place — when your hand stops at the table — what, actually, is doing the stopping?

You already have the answer ready. Something’s there. The table is full. The stuff of the table is in the way of the stuff of your hand. Fullness does the stopping.

Hold that thought exactly one more chapter. It’s the last piece of the old belief still standing, and it’s about to go.

Nothing at all, holding the line

Come back to Locke’s own example for a second, the one he was so sure of. Squeeze a blown-up ball between your hands and you’ll feel solidity, he said; the air inside pushes back, invincible, keeping your palms apart.

But notice what’s actually keeping your palms apart. Not a solid. Air. A thing so thin you can walk through it without a thought, a thing that is mostly, famously, nearly nothing. And yet trapped in that ball it shoves back on your hands as stubbornly as a stone. Locke used this to prove how universal solidity is — see, even air is solid enough! But turn it around and it starts to look like the opposite. If something so thin can hold your hands apart just as hard as a rock, then maybe the holding-apart was never really about how packed the space was. Maybe it was about something else — something that thin air has just as much of as a diamond does.

For the loudest possible version of this, leave the ball and go to a town square in Germany.

In 1654, a man named Otto von Guericke, the mayor of Magdeburg, built two hollow bronze bowls that fit together rim to rim into a hollow sphere. Nothing joined them — no glue, no bolts, no hooks, no thread. You could lift them apart with two fingers. Then he pumped the air out of the inside, so the sphere held as close to nothing as his pumps could manage. And he hitched a team of horses to each half and had them pull.

The horses could not do it. Straining teams of powerful animals, hauling in opposite directions, could not separate two metal bowls that were held together by nothing you could point to. There was no substance in the seam. There was no substance in the middle. Guericke ran the show again in front of the emperor himself, teams of horses on each side, heaving, and the empty sphere held.

What was holding it shut? Not stuff in the joint — the joint had nothing in it. The air outside was pressing in on every side, and inside there was almost no air pushing back out, so the outside won and clamped the halves together. The thing doing the gripping was pressure. A push. A force.

Now, be honest about what that push is made of, because it’s the objection that cracks this whole thing open if you don’t face it. The air outside isn’t “nothing” — it’s a crowd of countless tiny particles, and they hold the sphere shut by battering it from every side, a hail of little impacts. So isn’t this just stuff bumping stuff after all? Follow it down one more step. Ask why those air particles bump instead of passing through the bronze, and why they bump each other instead of merging — and you’re right back at the same question we started with, one level smaller. The bumping doesn’t explain the pushing. The bumping is pushing, wearing a smaller mask. Keep pulling that thread and every “bump” you meet turns out to be a shove across a gap. It’s force the whole way down. Magdeburg doesn’t show you stuff winning; it shows you that even a crowd of particles does its work by pushing, never by touching.

That’s the crack we’ve been walking toward. So maybe — and here’s the turn Newton’s question set up — maybe when your hand stops at the table, the table isn’t stopping you by being full of stuff in the way. Maybe it’s stopping you with a force, the same as the empty sphere, and the “fullness” was a story you told to explain a shove you couldn’t see.

That is exactly what the next man began to see.

Michael Faraday spent his life with electricity and magnets, watching forces reach across gaps and push and pull on things they never touched. And by 1844 he had followed that all the way down to a picture of matter that reads, even now, like science fiction. Forget tiny solid balls, he said. Picture instead that at the heart of each atom there is a center of force — a point from which pushing and pulling spread outward into the space around it. What we call a “particle” isn’t a hard little marble; it’s the busy region of force around such a center. And here’s the part that breaks the old belief clean in half: on this picture, Faraday wrote, “matter fills all space.” The force around every center reaches out and out, so there is no empty gap between atoms and no hard little surfaces to bump. Atoms don’t keep each other out by touching. They keep each other out by pushing — by force that acts across distance, the way Guericke’s outside air pushed, the way a magnet shoves another magnet away without contact.

Read what that does to the word “solid.” When you press your hand to the table and it stops, on Faraday’s picture nothing in your hand ever reaches anything in the table. The forces reach. The forces meet and shove. Your hand stops in midair, a whisper short of the wood, held off by a push with no substance in it — a tabletop-sized version of two magnets you can’t quite force together. The stopping is real. The touching is the illusion. Solidity, the most substantial-feeling thing in the world, turns out to be force wearing the mask of stuff.

Faraday, to be fair, was only guessing — and what he guessed at, a century of machines he never saw would go on to prove, though by a stranger road than he could have drawn.

You have never touched anything

Everything we’ve done so far, careful thinkers built with their eyes and their hands and their reasoning, over centuries. The last step took machines those thinkers couldn’t have dreamed of, and it turned Faraday’s strange picture into plain, measured, boring fact. It also aimed the whole thing straight at your own body.

Here is what a physicist today would tell you is going on right now, as you sit reading this.

Start with the atom, the thing you were taught is the little building block of all the stuff around you. An atom is almost entirely empty space. If you blew one up to the size of a big cathedral, the heavy part at its center — where nearly all the matter actually lives — would be about the size of a fly buzzing under the dome. Everything else, the whole vast volume of the atom, is essentially empty, with a faint haze of electrons spread through it. And you are made of these. The chair is made of these. Every “solid” thing you have ever leaned on is, by volume, something like 99.9999 percent nothing.

(Faraday, remember, said matter fills all space, and now I’m telling you the atom is nearly empty — but these fit together once you see that what fills the space isn’t little balls of stuff; it’s the reach of force and rule, spread thin over almost pure emptiness.)

So why don’t you sink through the chair like a stone through fog, since both of you are mostly empty and there’s so much room to pass?

Two reasons, and neither one is “the chair is full.” Here’s the first, and it’s stranger than any force: a plain rule of nature says the tiny bits of matter in you and the chair are not allowed to crowd into the same state. Electrons keep their own room, and they keep it absolutely — try to press two electron clouds into the same space and the rule fights back harder and harder, with a stubbornness that has nothing to do with bumping and everything to do with the bare fact that sharing that state is forbidden. That rule is a large part of why atoms have any size at all, and why matter doesn’t just collapse into its own emptiness. The second reason is the one Faraday guessed at: the electrons also carry a charge, and charge pushes on charge across the gap, an electric shove with no substance in it. Between them — a rule that says no sharing and a force that says keep back — your body is held a hair above the seat. Not by fullness. Not by contact. By a law and a push, working across a sliver of void, so that the surface you are certain you are pressing on, you never actually reach.

So look at what “solid” has become. The chair holds you up with a rule you cannot see and a force you cannot touch, reaching across a gap you cannot cross, between atoms that are themselves almost pure empty space. There is no fullness anywhere in that story. There is nothing “in the way.” You have never, in your whole life, touched the chair, or this book, or another human hand. You have felt a law and a push, always at a distance, always across a sliver of void — and if you want to insist that this, the meeting of forces, simply is what touching always was, then fine, but notice what you’ve had to give up to say it: the touching you meant, the one where two full surfaces actually meet, never happened and never could. Your skin, honest instrument that it is, reported “solid, full, in contact,” because a push is all it was ever built to notice.

Which means the very last piece of your original belief is gone. You said two things can’t share a place because they’re solid, and solid means full, and where there’s already stuff, no more fits. But there’s barely any stuff, it isn’t full, and the reason two things can’t share a place has nothing to do with a spot being already occupied. Two things keep apart because a rule forbids the sharing and a force does the pushing — across the emptiness, long before any “stuff” could ever be in the way.

Back in the workshop

Now go back to Florence, to the gold ball sweating water under the screws.

The first time through, it was just a curiosity — a soft thing beating a hard thing, the world being backwards for a minute. Look at it now and it’s the whole story in one image.

The men thought they could crush the water because they thought solidity was about fullness — pack the little parts closer, squeeze the stuff into less room. But the water’s parts weren’t sitting there full and idle, waiting to be shoved together. They were held apart, each one keeping its own room, refusing to close the gap — the same refusal that holds you off your chair. Turn the screws harder and you weren’t fighting stuff. You were fighting a law and a push, and neither one tires and neither one compresses. So the water did the only thing left: it kept its spacing exactly, and simply carried that spacing out through the tiny gaps in the gold — because the gold, too, was mostly gaps, a loose crowd of force-centers with room between them, not the seamless wall it pretended to be. The soft thing and the hard thing were the same kind of thing all along. Both were mostly empty. Both held their shape without ever quite touching themselves. The water just happened to find the doors first.

Nothing in that room was ever truly full. The gold wasn’t full; it let the water through. The water wasn’t full; it was almost all space. What crushed against the screws, what beaded on the surface, what those careful men mistook for the stubbornness of solid matter, was a rule and a force — the same ones holding you off your chair right now, holding Guericke’s sphere shut against the horses, standing in for a fullness that was never there.

The one fact you were surest of turns out to be the one place the world was fooling you the whole time. You live your whole life pressed up against things, certain you are touching them, certain they are full, certain that where they are, nothing else could be. And all of it — every knock and every catch and every closed door — is a law and a field of force over a great deal of empty space, telling your fingertips a simple, useful, lifelong lie.

You have never touched anything. And you never will. Consider, then, how much of the rest of what feels solid to you is holding you up the same way.